What is the Largest – Volume, Open –Top, Rectangular Box You can make from…. a sheet of paper, a piece of poster board a sheet of cardboard….

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Presentation transcript:

What is the Largest – Volume, Open –Top, Rectangular Box You can make from…. a sheet of paper, a piece of poster board a sheet of cardboard….

Making the box You can get many sheets of paper and try many different x’s. You can cut and fold repeatedly and find the x by trial and error. For your first x – let’s say x = 0.5 inch, then try 1.0 inch, and repeat as necessary to find the largest volume. 11 inches 8.5 inches x

Try it on the internet Try it: Each time you click the “cut and fold” button, the applet folds up the box and tells you its volume and surface area. By trial and error, find the x that produces the largest volume.

Let’s make a chart: (Use your Graphing Calculator) X-value (in inches) Length (in inches) Width (in inches) Volume of Box L1L2L3L in in in in in in in 3 6.0in

What is the maximum volume of the box according to this chart?

What happens if our increment gets smaller? What do we need to change? Is there a faster way to accomplish this?

Write the function and determine its domain.